1. Field of the Invention
The present invention relates to a method of calculating the amount of fluctuation of an imaging characteristic of a projection optical system, an exposure apparatus, and a method of fabricating a device.
2. Description of the Related Art
A reduction projection exposure apparatuses are used in processes of fabricating semiconductor devices. The reduction projection exposure apparatuses illuminate a mask (reticle) using light from a light source so as to project an image of a pattern formed on the mask onto a wafer, onto which a photoresist has been applied, with the size of the pattern reduced.
Japanese Patent Laid-Open No. 2003-203853 (referred to as “reference 1” hereafter) describes an exposure apparatus with which a substrate is exposed to exposure light of two wavelength bands. When the exposure light of two wavelength bands is used, a resist applied onto the substrate can be exposed to an increased amount of exposure light. However, the amount of energy exerted on a projection optical system is also increased. It is known that optical characteristics such as a refractive index of the projection optical system, when the projection optical system absorbs part of exposure energy, fluctuates due to temperature change in the projection optical system caused by heat produced through the absorption of the exposure energy.
When the projection optical system continuously operates with the exposure light for a long time or operates with the exposure light of high illuminance, fluctuation of the optical characteristics of the projection optical system increases. Illuminance is generally understood as the amount of luminous flux incident on a surface per unit area. As a result, fluctuation of imaging characteristics of the projection optical system such as aberrations, focusing, and magnifications increases, thereby causing non-negligible amounts of defocusing and misalignment to occur. In order to suppress such fluctuations, methods of correcting fluctuation of imaging characteristics of the projection optical system being exposed to exposure energy have been proposed (reference 1 and Japanese Patent Publication No. 8-21531 (referred to as reference 2 hereafter)).
According to reference 1, fluctuation information presenting the relationships between the amount of time, for which the projection optical system is irradiated with the exposure light, and the amount of fluctuation of aberration is obtained in advance for wavelength bands including the wavelengths of the exposure light (for example, a wavelength of the i-line or bandwidth including the g-line, h-line, and i-line), and imaging characteristics of the projection optical system are corrected using the fluctuation information.
Reference 2 describes a computation of the amount of fluctuation using a model expression (function) that represents the amount of fluctuation of an imaging characteristic of the projection optical system.
The fluctuation information described in reference 1 is obtained in advance for wavelength bands including exposure light and stored in a storage device. The amount of fluctuation of the imaging characteristic of the projection optical system changes when the wavelength band and the intensity of the exposure light to be used change. For this reason, with the technology described in reference 1, the amount of fluctuation of the imaging characteristic of the projection optical system can be estimated only when the exposure light is of a wavelength band and light intensity obtained in advance. That is, changes in wavelength band and light intensity are not considered, and accordingly, there is an error in estimating the amount of fluctuation in the case where the wavelength or the light intensity changes.
According to the technology described in reference 2, the wavelength band of the exposure light is not considered, and accordingly, it is impossible to obtain the amount of fluctuation of an imaging characteristic of the projection optical system corresponding to the wavelength band of the exposure light.
Thus, with respect to an imaging characteristic of the projection optical system, there may be an error occurring between the estimated amount of fluctuation and an actual amount of fluctuation, and highly precise correction of the imaging characteristic of the projection optical system cannot be performed.